Joint Colloquium: Tillman -- The complexity of 3-manifolds

JOINT COLLOQUIUM 

Friday, August 14, 2 PM 

Room 3084 in the Red Centre, University of New South Wales 

Stephan Tillman, University of Queensland 

The complexity of 3 manifolds 

The complexity of a 3-manifold is the minimum number of tetrahedra in a triangulation of
the manifold.  It was defined and first studied by Matveev in 1990.  The complexity is
generally difficult to compute, and various upper and lower bounds have been derived
during the last decade using fundamental group, homology or hyperbolic volume.  

Effective bounds have only been found recently in joint work with Jaco and Rubinstein.
Our bounds not only allowed us to determine the first infinite classes of minimal
triangulations of closed 3-manifolds, but they also lead to a structure theory of
minimal triangulations.  

In this talk, I will give a general introduction to complexity of 3-manifolds and
explain its ramifications for algorithmic problems in the study of 3-manifolds.  

please contact me carberry@maths.usyd.edu.au if you are planning to attend and either
need or can offer a lift.  We will take the Speaker to lunch beforehand; exact lunch
plans are yet to be determined.